Polynomial surface

The idea first is to compute integral.
It is also by extension a lib(libpolysurf) with many others features :

• Sign study
• Roots finder
• Intersection
• ...

Requirements

• gmp
• mpfr
• CUnity/Cunit

Releases

• v1.0 : Highest tested order 48.
• v2.0 : Highest tested order gmp(mpz_t) 4096.
• v2.1.0 (prerelease) : Highest tested order mpfr(mpfr_t).

Build

all

./build.sh

build

make

clean

make clean

Doc

Generate to doc/html folder.

make doc

Usage surfaces

Overview

./surfaces 

Detail

./surfaces -?

Default interval [0..5]

./surfaces 3+x+2x^3

Custom interval [0..10] by short options

./surfaces -l0 -h10 3+x+2x^3

Custom interval [-10..10] by long options

./surfaces --low=-10 --high=10 3+x+2x^3

Custom interval [-10..10] with ratios by short options

./surfaces -l-10 -h10 1/3+2/3x+2/5x^3

Same as previous with raw result output

./surfaces -v0 -l-10 -h10 1/3+2/3x+2/5x^3

Note on multiple precision (max order > 48) you can change :

• AP engine (0 for gmp int or 1 for mpfr float) with -e option
• Precision with -p option

You can display the raw result with -v0 option.
Typically messed up with exp greater than POLY_MAX_ORDER leading to buffer overflow

./surfaces -l-10 -h10 3+4x^2+x^16384
munmap_chunk(): invalid pointer
Abandon

or for french people

./surfaces -l-10 -h10 3+4x^2+x^16384
Exception en point flottant

Change related define in main to allow higher exp.

Performance

Read Security-related flags and options for C compilers to know more.

If you activate the sanitizer options on compiler for debug purpose you will see some LeakSanitizer errors, it's a false positive because gmp lib allocation/free process is asm based and not managed by libasan.

Accuracy

Polynomial surface is optimized from higher order as below :

• o < 2 => middle point method.
• o < 4 => simpson method (aka rk4).
• o < 48 => antiderivative Δ.
• o > 48 => antiderivative mp Δ.

Tests

• Based on CUnity/Cunit framework.
• Organized by suite => a suite is a domain feature.
• See tests report below.

Build sources (fresh release v3.2.7), clone repo and follow the Readme.
Then

make
sudo make install

Build tests from root project.

make
make test

to run tests with or without options (bci)

./surfaces_test <options>

Clean tests from root project.

make cleantest

Tests report

Run Summary       -      Run    Failed  Inactive   Skipped
     Suites       :        8         0         0         0
     Asserts      :   173413         0       n/a       n/a
     Tests        :       81         0         0         0

Lib polysurf

Compile lib.

make lib

Install lib.

sudo mkdir -p /usr/include/libpolysurf
sudo cp include/*.h /usr/include/libpolysurf
sudo cp libpolysurf.so.1.0 /usr/lib
sudo ln -s /usr/lib/libpolysurf.so.1.0 /usr/lib/libpolysurf.so
sudo chmod 0755 /usr/lib/libpolysurf.so
sudo ldconfig

Examples polysurf

Can be found in src/examples.

make examples
export LD_LIBRARY_PATH=.

example intersect usage

$./ex_intersect 3 2
     No intersection

$./ex_intersect 2x 2x-1
     No intersection

$./ex_intersect 5x-10 4x+4
     p0(14.0000000000000000 , 60.0000000000000000)

$./ex_intersect 2x^14-100 3x^12+10
     p0(-1.4542375034682683 , 278.3770290295971449)
     p1(1.4542375034682683 , 278.3770290295971449)

$./ex_intersect 2x^401 4x^4000
     p0(0.9998074241631791 , 1.8513532041527613)

Extra

Alternatives methods with no reliability are tested here.

• Riemann sums(left,right,rect,trapezoid,midpoint).
• Simpson rules.
• Newton-cote.

Todo

• implement integral factory tests for mpfr.
• add features in lib polysurf.

Contribute

• open to pull requests, rule is 1 mod => 1 unit test (TDD).

Licence

• GNU3 GPL(not LGPL).
• That means you can reuse a part or the whole for non commercial project.
• For other cases, pls contact me.

Links

• Area Under a Curve
• Rieman sum calculator
• Ratio addition
• Online integral calculator
• Symbolab online IC with ratios result

Tools

To validate results while testing I used these tools :

• the powerfull bc
• geogebra